Numerical solution of multi-variable cell population balance models: I. Finite difference methods

Multi-variable cell population balance models represent the most accurate a nd general way of describing the complicated phenomena associated with cell growth, substrate consumption and product formation due to the level of de tail included in them. Therefore, the ability to solve and understand such models is of fundamental importance in predicting and/or controlling cell g rowth in processes of biotechnological interest. However, due to the fact t hat such models typically consist of first-order, partial integro-different ial equations coupled in a nonlinear fashion with ordinary integro-differen tial equations, their solution poses a serious challenge. In this work, we have developed several finite difference algorithms for the solution of the problem in its most general formulation (i.e. for any set of single-cell p hysiological state functions). The validity of the developed algorithms was verified by comparing their results with those of three specific test prob lems for which several solution characteristics are known. Moreover, the nu merical schemes were compared to each other with respect to their key numer ical features, such as stability, accuracy and computational speed. Solutio ns of the cell population balance model with up to three state variables we re obtained using a Pentium II 450 MHz PC in tractable CPU times. (C) 2001 Elsevier Science Ltd. All rights reserved.